In terms of the opportunity to clarify these concepts, consider this example

void fun(int&){}  // #1
void fun(int){}   // #2
int a = 0;
fun(a);

The identity conversion is vague here. Since using a glvalue a to initialized the parameter at #2 with type int, the conversion comprises "lvalue-to-rvalue conversion" as per the order defined in [conv.general] p1, now the result is a prvalue of type int, since the definition of [conv.qual], from a prvalue of type int to a prvalue of type int is qualification conversion. Instead, for #1, we explicitly say it is an identity conversion in [over.ics.ref] p1. Hence, as per [over.ics.rank#3.2.1], #1 is the best viable function? Actually, the implementations report ambiguity.

This issue arises from when we step into [conv#general-1.4]

Zero or one qualification conversion.

How should we treat them where whether, from a prvalue of type T to the same type, is necessary to be considered qualification conversion?

Back to the definition of identity conversion, the relevant notes and normative rules are
[over.ics.scs#2]

As described in [conv], a standard conversion sequence either is the Identity conversion by itself (that is, no conversion) or consists of one to three conversions from the other four categories.

[conv#general-note-1]

A standard conversion sequence can be empty, i.e., it can consist of no conversions.

[over.best.ics#general-8]

If no conversions are required to match an argument to a parameter type, the implicit conversion sequence is the standard conversion sequence consisting of the identity conversion ([over.ics.scs]).

Does it mean, even though an lvalue-to-rvalue conversion applies and the result prvalue with the same type as that of the target, it cannot be considered as identity conversion? Moreover, from a prvalue of type T to the same type, it can also be considered as qualification conversion, so it is also not identity conversion?

Clarification, I think we should give a terminal condition of implicit conversion(i.e., standard implicit conversion) to avoid the endless conversion that is permitted on concept or definition.

int a =0;
int const volatile t = a; // just lvalue-to-rvalue conversion

Even though we say a standard conversion sequence can consist of one to three conversions from the other four categories, and a qualification conversion is permitted by the concept. In other words, we should give a condition to avoid it go into [conv#general-1.4] if that condition is satisfied.

I think the intent is that all conversions described in [conv] are not "empty".

This is clear in the formulation of integral and floating-point conversions, where we say "another ... type". Which didn't properly exclude mere differences in cv-qualification (first patch in this pull request). Similarly, [conv.qual] should only allow conversions to a different type, excluding a conversion from T to T (second patch in this pull request).

Please still consider [conv.qual], give such two example

const volatile int v = 0;  // #1
const volatile Class obj = Class();  // #2

The target type of #1 and #2 are all cv-qualified types. Consider #1, as per [dcl.init#general-15.9], a standard conversion sequence will be used if necessary, although the fixed [conv.integral] has rejected to be used, however, [conv.qual] still permit to be used if they are different types. Is there necessary to convert int to const volatile int by a qualification conversion? Presumably, it's not necessary, #2 is also similar. In these cases, a prvalue of cv1 T is sufficient to initialize the object of cv2 T, a qualification conversion is not necessary here. If it would be permitted, it will impact [over.rank]. More generally, I think [conv.qual] is meaningful to be used only in the case that the cv-qualifiers other than cv0 of two similar types are different.

I think there are situations where the need for a top-level qualification-conversion is significant:

int f(int &x);
int f(const int& x);
int a;
int y = f(a);  // selects f(int&)

Note also that forming a conversion sequence in overload resolution is different from the actual initialization in [dcl.init]. For the actual initialization, [dcl.init] should (does it?) ignore top-level cv-qualifiers on the target.

IMO, regardless of the first or second overload, the parameters are all of the reference type, a valid reference type cannot be cv-qualified, in this case, the rank is impacted by [over.ics.rank#3.2.6], that rule explicitly says we talk about the top-level cv-qualifiers of the referenced type. I think the qualification conversion is almost prepared for pointer types and their top-level cv-qualifiers do not have an effect.

int* ptr = 0;
int* const ptr1 = ptr // lvalue-to-rvalue conversion is sufficient

int const* ptr2 = ptr // lvalue-to-rvalue conversion followed by a qualification conversion

Hence, we can generally say qualification conversion is not necessary to apply to two similar types where their difference only in cv0(i.e. the top-level cv-qualification of that type).

[dcl.init] should (does it?) ignore top-level cv-qualifiers on the target.

I'm not clear about whether the initialization is or not, however, for overload resolution, the top-level cv-qualifiers are ignored once the function type has formed. In the initialization case, the target type is defined as.
[dcl.init#general-15]

The destination type is the type of the object or reference being initialized and the source type is the type of the initializer expression. If the initializer is not a single (possibly parenthesized) expression, the source type is not defined.

It could arguably say the top-level cv-qualifier is considered in the destination type.